Analysis and design for ill-conditioned plants

Abstract

A study of the robust performance problem when the plant transfer function is ill-conditioned is made. This is achieved by studying the equivalent problem of robust stability against simultaneous perturbations at plant input and output; the appropriate robustness test for this problem is Doyle's structured singular value. Bounds upon the structured singular value that display the interrelation between plant directionality properties, design specifications, and the compensator are derived. The procedure reveals that certain parameters, which we term'coupling coefficients', play a critical role in determining whether a feedback system with an ill-conditioned plant can be destabilized by small simultaneous perturbations. Perturbations that potentially cause instability are also identified. A simple special case is studied for which the coupling coefficients and problematic perturbations have straightforward and intuitively plausible interpretations.